Re: class and inviduals

> 
> 
> -------- Original Message --------
> Subject: Re: class and inviduals
> Resent-Date: Sat, 20 Nov 2010 22:41:25 +0000
> Resent-From: public-owl-dev@w3.org
> Date: Sat, 20 Nov 2010 22:39:03 +0000
> From: Bijan Parsia <bparsia@cs.man.ac.uk>
> To: public-owl-dev@w3.org
> CC: Birte Glimm <birte.glimm@comlab.ox.ac.uk>
> 
[snip]
> 
> See my example above. OTOH, perhaps the Birte et al approach does this and does it at the cost of a linear number of additional axioms. It's not 100% clear to me (though I've not read the paper very carefully yet). This is possible as they don't apply Hilog semantics to roles. If so, then it's a lot cheaper (and easier to implement) than I had thought. Indeed, it could be implemented via preprocessing. Hmm.
> 
> Ok, Table 3 sorta convinces me that that would work. If I make O_houseMouse same as O_fieldMouse,then...ok, no, I've lost it :) I see that you'd get the  MatSubClass axiom: Class ⊓∀type− .∃type.{oC }≡Class⊓ ∃subClassOf.{oC} since those oCs are individuals. Equality there will substitute. But I don't see how we'd get back to C equiv D.
> 
> Oops! Wait, Theorem 1 claim 1 rules it out, as all axioms in the signature of the original ontology entailed by the metamodelling enabled ontology are entailed by the original ontology. Thus, we don't get from C=D to C equiv D.
> 


Let me step in for Birte here (as I co-authored the paper). In fact, Theorem 1 just states that if you just rewrite the KB in the presented way, the consequences on the original vocabulary do not change. However, if you additionally postulate axioms on the extended (reified) vocabulary this will change things. In particular if you assert o_houseMouse same as o_fieldMouse, this will have exactly the effect that Bijan assumed, namely extensional equivalence of the two classes. Feel free to check with any OWL-compliant reasoner.

Cheers,
  Sebastian



_________________________________________________
Dr. Sebastian Rudolph
senior researcher & project leader at AIFB
Karlsruhe Institute of Technology (KIT)
rudolph@kit.edu                    phone +49 721 608 - 7362
www.sebastian-rudolph.de        fax +49 721 608 - 5998